A Stochastic Approach to the Subset Selection Problem via Mirror Descent

The subset selection problem is fundamental in machine learning and other fields of computer science.We introduce a stochastic formulation for the minimum cost subset selection problem in a black box setting, in which only the subset metric value is available.Subsequently, we can handle two-stage schemes, with an outer subset-selection component and an inner subset cost evaluation component. We propose formulating the subset selection problem in a stochastic manner by choosing subsets at random from a distribution whose parameters are learned. Two stochastic formulations are proposed.The first explicitly restricts the subset's cardinality, and the second yields the desired cardinality in expectation.The distribution is parameterized by a decision variable, which we optimize using Stochastic Mirror Descent.Our choice of distributions yields constructive closed-form unbiased stochastic gradient formulas and convergence guarantees, including a rate with favorable dependency on the problem parameters.Empirical evaluation of selecting a subset of layers in transfer learning complements our theoretical findings and demonstrates the potential benefits of our approach.